Munich Personal RePEc Archive

Credit Expansion, the Prisoners

Dilemma, and Free Banking as

Mechanism Design

van den Hauwe, Ludwig

21 February 2008

Online at https://mpra.ub.uni-muenchen.de/12991/

MPRA Paper No. 12991, posted 25 Jan 2009 06:12 UTC

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Credit Expansion, the Prisoner�s Dilemma, andFree Banking as Mechanism Design

By: Ludwig van den Hauwe (*)

Resumen

A pesar del car�cter distintivo del enfoque austr�aco de las “microfundaciones para la macroeconom�a”, la literatura sobre la banca libre contiene algunos argumentos que recurren a los conceptos y modelos de la teor�a de juegos tales como el conocido modelo Dilema del Prisionero. A pesar de que no puede existir una presunci�n a priori sobre la posible utilidad de conceptos de la teor�a de juegos para las teor�as austr�acas, en el contexto del debate sobre la banca libre tales conceptos y modelos han sido manejados con distintos grados de perspicacia. Un ejemplo elaborado en el documento comenta la configuraci�n de interacci�n entre los bancos independientes en un sistema de banca libre con reserva fraccionaria, que a veces ha sido modelado como un juego de Dilema del Prisionero One-Shot. Esta conceptualizaci�n no ofrece suficientes argumentos para la tesis de la sobreexpansi�n in-concert, ni para la tesis de que un sistema de banca libre con reserva fraccionaria tender�a a la creaci�n de un banco central. El autor abandona la asunci�n impl�cita de que existe una correspondencia de uno a uno entre la matriz de resultado y la matriz de utilidad. Al reconocerse que los bancos en un sistema de banca libre con reserva fraccionaria no deben adoptar necesariamente una perspectiva “miope” y ego�sta, pero pueden reconocer la armon�a de intereses a largo plazo entre el sector bancario y la sociedad en general, surgen una conceptualizaci�n y representaci�n de la matriz distintas.

Palabras claves: Dise�o de mecanismo econ�mico; Teor�a del ciclo de

negocios; Dilema del Prisionero; Banca libre.

Abstract

Despite the distinctive character of the Austrian approach to “microfoundations for macroeconomics”, the literature on free banking contains a number of arguments which make use of game-theoretic concepts and models such as the well-known Prisoner�s Dilemma model. While there can be no general a priori presumption against the possible usefulness of game-theoretic concepts for Austrian theorizing, in the context of the debate on free banking such concepts and models have been used with varying degrees of perspicacity. One example which is elaborated in the paper is concerned with the interaction configuration between independent banks in a fractional-reserve free banking system, which has sometimes been modeledas a One-Shot Prisoner�s Dilemma game. This conceptualization does not provide a sufficient argument for the in-concert overexpansion thesis, nor for

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the thesis that fractional-reserve free banking will tend to lead to the establishment of a central bank. The author drops the implicit assumption that there exists a one-to-one correspondence between the outcome matrix and the utility matrix. When it is acknowledged that banks in a fractional-reserve free banking system need not necessarily adopt a “myopic”, self-regarding perspective but may recognize the long-run harmony of interests between the banking sector and society at large, a different conceptualization and a different matrix representation emerge.

Keywords: Economic Mechanism Design; Business Cycle Theory;

Prisoner�s Dilemma; Free Banking;

JEL Codes

D01, E31, E32, E42, E52, E58, E66, G18, K39

1. Introduction -

1.1. The institutional turn in business cycle theorizing -

Different causal explanations of the business cycle typically lead to

different sorts of policy advice. Whereas the new classical economists had

essentially made a case against discretionary policy activism and in favour of

rules, based on a set of arguments including the policy ineffectiveness

proposition, the Lucas critique and time inconsistency, thus providing a

sustained challenge to the monetarist as well as the Keynesian orthodoxies,

the new Keynesian school has provided rigorous microfoundations to explain

why markets may fail to clear due to wage and price stickiness, thus

accounting for involuntary unemployment as an equilibrium phenomenon

and providing a rationale to justify interventionist policies to stabilize the

economy.

Remarkably none of these better known paradigms has provided a

fundamental criticism of the prevailing monetary-institutional framework.

Among the various conceptualizations of business cycle phenomena and the

concomitant policy and/or reform proposals only the Austrian paradigm

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occupies a unique place on account of the truly radical character of its

proposals for institutional reform.

Since on the Austrian account of boom and bust, the bust is simply

the market�s recognition of the unsustainability of the previous credit-

induced boom, the Austrians� policy advice to the central bank would consist

of prevention rather than cure: do not engage in credit expansion in the first

place.1 But since abiding by this imperative is notoriously difficult both

politically and technically, what is apparently needed is fundamental reform

rather than policy prescription. Beginning with Hayek�s 1976

Denationalisation of Money several attempts have been made, by Austrian

economists and fellow travelers, to provide theoretically possible and

consistent alternatives to existing central banking regimes. While some

degree of variation can be discerned among the different proposals, the

common thread in these proposals consists is an argument to the effect that

nothing less than a thoroughly decentralized banking system, one in which

the market rate of interest is an unbiased approximation of the natural rate,

may be the ultimate solution to the problem of boom and bust.

The search for institutional alternatives to prevailing central banking

regimes has thus led to a closer examination of the hypothetical working

characteristics and the internal dynamics of possible systems of “free”

banking, that is to say decentralized and non-hierarchical monetary systems

in which banks would engage in the competitive supply of money. According

to one such proposal, developed by, among others, L. White (1989; 1995), G.

Selgin (1988) and L. Sechrest (1993), in the free banking system market

mechanisms would move each of the unprivileged private banks which would

engage in the unrestricted competitive issue of specie-convertible money, as

well as the banks as a group, toward equilibrium and would so restrain them

from over-issuing. Monetary instability and business cycles as they typically

result from central- bank activity would disappear.

The superiority of a fractional-reserve free banking system is

perceived as being related to the speed with which the self-correcting

mechanism operates to reverse an over-issue by any single bank. Under the

free banking system of multiple competing note issuers, the check against

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over-issues by any single bank is more rapid and direct, because of the

negative feedback provided by interbank clearings. Under a central banking

system of a single monopoly note issuer, the check against excessive note

issue is attenuated; the corrective process is likely to take more time before

it exercises its discipline on the central bank. In the meantime the central

bank may have sufficient time to generate an artificial boom through the

injection of new money. (White 1995) Accordingly credit expansion would be

more limited and kept within narrower boundaries under fractional-reserve

free banking than may be the case under central banking.

The proposal of a system of fractional-reserve free banking has been

challenged, however, by authors who advocate a return towards a 100 per

cent reserve requirement in banking. According to these authors the alleged

advantages of fractional-reserve free banking are largely if not entirely

illusory. It is claimed by these authors that fractional-reserve free banking

would be inherently unstable, foster credit expansion and thus “inevitably”

lead to the introduction or the re-introduction of a central bank. The only

mechanism which can render the monetary system proof against recurring

boom-bust cycles is a 100 per cent reserve requirement.

In order to better understand the rationale of various proposals of free

banking as well as the radical nature of the proposals for institutional reform

which have been proposed within the Austrian paradigm, we have to

appreciate the causal role of credit expansion within the Austrian account of

boom and bust.

1.2. How credit expansion creates an unsustainable mix of

incompatible market forces

Despite its considerable explanatory power and its relevance for the

comprehension of real-world phenomena, the Austrian theory of the

business cycle had remained comparatively unknown until quite recently. In

conventional overviews of developments in business cycle theory since

Keynes� General Theory, the theory was on occasion mentioned in an

introductory section devoted to the “History of Business Cycle Theory”, or

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Hayek was mentioned in an appendix explaining “The Over-investment

Theory”. (see e.g. Arnold 2002) Since some time this situation has begun to

change. As a result of the important contributions of R. W. Garrison (among

others), it is today no exaggeration to assert that in the global

macroeconomic landscape the Austrian macroeconomic school has acquired

a respectable place among the various other macroeconomic schools and

paradigms, and that it is there to stay.

In the capital-based account of the business cycle, credit expansion

figures prominently as a causal factor underlying the boom-bust sequence.

According to the Austrians, the market is capable of allocating resources in

conformity with intertemporal preferences on the basis of a market-

determined (natural) rate of interest. It follows, then, that an interest rate

substantially influenced by extra-market forces will lead to an intertemporal

misallocation of resources. The capital-based theory of the business cycle is

thus a theory of boom and bust with special attention to the extra-market

forces that initiate the boom and the market�s own self-correcting forces that

turn boom into bust.

In the case of an artificial boom, the change in the interest-rate signal

and the change in resource availabilities are at odds with one another. To

the extent that the central bank pads the supply of loanable funds with

newly created money, the interest rate is lowered just as it is with an

increase in saving, but in the absence of an actual change in time

preferences, no additional resources for sustaining the policy-induced boom

are being made available. In fact, facing a lower interest rate, people will save

less and spend more on current consumables. Seemingly favourable credit

conditions encourage the initiation of long-term investment projects at the

same time that the resources needed to see them through to completion are

being consumed. Consumers and investors become engaged in a tug-of-war.

The central bank�s credit expansion drives a wedge between saving and

investment. It results in an incompatible mix of market forces. The artificial

boom is thus characterized by malinvestment and overconsumption. (Mises

1998) In terms of a familiar device introduced by Hayek and often used in

expositions by Austrian macroeconomists, we can say that the triangle is

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being pulled at both ends against the middle. The now familiar graphical

depiction of a policy-induced boom-and-bust cycle combines the Hayekian

triangle and the simple analytics of the loanable funds market with the

Garrisonian production possibilities frontier. It is displayed in figure 1.1.

The wedge driven between saving and investment in the loanable funds

market and the tug-of-war that pulls the economy beyond its production

possibility frontier are manifested in the economy�s capital structure as

clashing triangles. In the case of a saving –induced capital restructuring, the

derived-demand effect and the discount effect work together to reallocate

resources toward the earlier stages. In the case of credit expansion, the two

effects work in opposition to one another.

Figure 1.1

A Policy-Induced Boom and Bust

Stages of Production

Interest Rate

Saving

ieq Saving plus Credit

i� Expansion

Investment

S=I S,I

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The time-discount effect, which is strongest in the early stages, attracts

resources to long-term projects. These excessive allocations to long-term

projects are called malinvestment in the Austrian literature. The derived-

demand effect, which is strongest in the late stages, draws resources in the

opposite direction so as to satisfy the increased demand for consumer goods.

The malinvestment is therefore accompanied by overconsumption. In the end

real resource constraints remain binding, however, and a bust is the

eventual but inevitable resolution to the problem.

1.3. The search for adequate micro-foundations

It is today commonplace to point out that macroeconomics should be

grounded in choice-theoretic microfoundations. Whereas the new classical

approach had put a strong emphasis on underpinning macroeconomic

theorizing with neoclassical choice-theoretic microfoundations within a

Walrasian general equilibrium framework and had thus basically consisted

in adapting macro theory to orthodox neoclassical market-clearing

microfoundations, the new Keynesian theorists, while they agree that

macroeconomic theories require solid microeconomic foundations, have also

recognized the importance of a whole variety of real-world imperfections.

Problems associated with asymmetric information, heterogeneous agents

and imperfect and incomplete markets etc. are not assumed away. They have

thus basically preferred to adapt micro to macro theory.

These relatively recent developments should not blind us to the fact

that, as regards the recognition of the need for macroeconomic theories to be

grounded in microeconomic foundations, the Austrian economists were

clearly precursors. Methodological individualism and a rejection of excessive

macro-economic formalism have been constant themes in Austrian

methodological writings.2 While Austrian macroeconomists in general thus

do not question the now mainstream consensus regarding the need or at

least the desirability of providing macroeconomic theories with adequate

choice-theoretic foundations, this stance has often been accompanied by the

proviso that their own variant of microeconomics – designated as Mengerian

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or as praxeological – should be clearly distinguished from the neoclassical

variant. Austrians have thus on occasion highlighted the peculiar character

of their own approach to the issue of “microfoundations for

macroeconomics”.

It should immediately be noted, however, that this stance has not

always been consistently maintained. For instance while various

argumentative strategies have been used in the context of the debate on free

banking, the advocates as well as the opponents of fractional-reserve free

banking, in their attempts to scrutinize the actual incentives toward credit

expansion that the banks would face within a fractional-reserve free banking

system, have on occasion resorted to arguments drawn from game theory

and in particular to the interaction configuration known as the Prisoner�s

Dilemma. The fact that the same game-theoretical model is used by

participants on both sides in a debate in order to support divergent

conclusions – in casu concerning the working characteristics of fractional-

reserve free banking - is sufficiently remarkable in itself to warrant a closer

examination of the respective arguments. Is it true that game theory, and in

particular the Prisoner�s Dilemma model, are basically “a gun for hire”,

which can be used almost ad libitum for various purposes, as some have

claimed, or is it possible to unambiguously distinguish between correct

applications of the Prisoner�s Dilemma and incorrect ones in this

connection? In the remainder of this paper it will appear that Prisoner�s

Dilemma game type of arguments have been used with varying degrees of

perspicacity.

1.4. The multifarious uses of the Prisoner�s Dilemma model in

economics

The applications in theoretical and applied economics of the

interaction configuration which is known in game theory as the Prisoner�s

Dilemma are varied and numerous. Formally, a game with two or more

players is a Prisoner�s Dilemma if each has a unique dominant strategy and

an inefficient outcome results when each plays his or her dominant strategy.

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(Campbell 2006, 47) The Prisoner´s Dilemma is the paradigmatic example of

self-interested, rational behavior not leading to a socially optimal result.

(Mas-Colell et al. 1995, 237) A conventional representation of the pay-off

structure of the Prisoner´s Dilemma game is depicted in figure 1.2.

The outcome matrix represents a Prisoner´s Dilemma if and only if Player A´s

preference ordering of the outcomes is P > Q > R > S, and Player B´s

preference ordering is S > Q > R > P.

Figure 1.2

The Prisoner´s Dilemma is not an Austrian invention, however.3

In view of the Austrians´ more or less outspoken preference for Mengerian

microfoundations, the recurrent use of Prisoner´s Dilemma type of

arguments in Austrian writings may at first seem somewhat remarkable. On

occasion one finds in the work of one and the same author a defense of

Austrian and in particular Mengerian microfoundations as well as explicit

arguments invoking a game-theoretical model such as the Prisoner´s

Player B

C D

C Q: 3 , 3 S: 1 , 4

Player A

D P: 4 , 1 R: 2 , 2

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Dilemma. An example is provided by Horwitz´ (2000) Microfoundations and

Macroeconomics. Despite his endorsement of a Mengerian approach to

microeconomics as the foundations for macroeconomics and of a Mengerian

conception of the competitive process, this author repeatedly invokes the

Prisoner´s Dilemma in his explanation of why economy-wide changes in

prices necessitated by monetary disequilibrium are problematic.

Each individual seller would like to cut prices when faced with slackening

sales, but none is willing to do so without some assurance that other sellers

will do the same. The result is therefore sub-optimal: no one cuts prices

when everyone should. (e.g. Horwitz 2000, 145) The falling price level is a

public good of sorts and each actor wishes to reap the benefits of the needed

decline, but no one is able to bear the cost of starting the process. With

everyone trying to free ride off the desired result, it never occurs. No

individual has an interest in doing what would, if done collectively, benefit

all. This, Horwitz argues, is a classic Prisoner´s Dilemma. (ibid. 158)

The major advantage of fractional-reserve free banking, Horwitz

pursues, is precisely that it does adjust the nominal quantity of money to

equilibrate potentially devastating monetary disequilibria rather than leaving

that burden to the price level. One central shortcoming of 100 per cent

reserve banking, according to this author, is that it is unable to do this and

that it relies on the price level to bear the burden of adjustment. (ibid. 229)

Clearly in this instance the Prisoner´s Dilemma model is used in an attempt

to justify credit expansion by the fractional-reserve free banking system.

It is doubtful whether this argument is supported by conventional

price theory and whether the underlying hypothesis of pervasive price

stickiness, even in the absence of institutional barriers to price flexibility, is

indeed descriptive of real-world situations. Besides these obvious

reservations, it should be clear why Horwitz´s who-goes-first argument,

especially when considered as an argument for the superiority of a

fractional-reserve free banking system in comparison with a system based on

a 100 per cent reserve requirement, is not convincing.

According to monetary disequilibrium theorists such as Horwitz, not

the price rigidities per se but deflationary pressures constitute the

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originating factor of depressions. Excess demands for money and not price

rigidities are the originating factor of depressions. Furthermore, the

monetary disequilibrium theorists argue that excess demands for money

need not lead to depression and unemployment, if the monetary system

responds quickly to such excesses by creating additional nominal supplies of

money. There are several problems with this view.

A first objection consists in pointing out that if there

exists something like a who-goes-first problem, a policy of accommodating

excess demands for money might worsen it because of a moral-hazard type

of problem.

Furthermore the conclusion of Horwitz, considered as an argument

against the 100 per cent reserve requirement in banking, is clearly flawed for

the following reasons. When monetary disequilibrium theorists like Horwitz

refer to downward pressures upon the general price level due to excess

demands for money they mostly implicitly have in mind the kind of special

circumstances as they prevail in a fractional-reserve banking system when

excess demands for money actually trigger a decline - or a collapse - of the

money supply because of a phenomenon known as multiple deposit

contraction. It is indeed the multiple-contraction effect that actually

accounts for the generalized nature of the phenomenon. A particularly

dramatic instance of this phenomenon relates to the financial difficulties

prevailing at the time of the onset of the Great Contraction and significantly

Horwitz himself mentions this example.4

In Chapter 5 of his (2000) Microfoundations of Macroeconomics, entitled

Monetary equilibrium theory and deflation (141-175), and to which he refers

on page 228 when criticizing 100 per cent reserve banking for not offering a

satisfactory solution to Prisoner�s Dilemma problems due to excess demands

for money, Horwitz writes:

“(…) prior to the Great Depression, the US economy was able to

avoid significant unemployment for any real length of time

precisely because wages were relatively free to adjust

downward when needed. The Great Depression brought an end to

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that policy, as bad economic ideas and the self-interest of

labor and politicians led to calls for maintaining nominal

wages in the face of a 30 percent decline in the money supply.

It is of little surprise that the result was 25 percent

unemployment, a failure of one-third of US banks, and

widespread business bankruptcies.”(ibid. 164)

However, these kinds of special circumstances would

never and can never occur under a system of 100 per cent reserve banking.

Under 100 per cent reserve banking a 30 per cent decline in the money

supply could never have happened in the first place. Therefore Horwitz�s

attack upon the advocates of 100 per cent reserve banking is flawed. It will

be recalled what the charge against 100 per cent reserve banking is. The

criticism starts from a distinction, connected with the so-called productivity

norm, between falling prices necessitated by declines in income velocity

unmatched by increases in the nominal money supply and falling prices

caused by increases in factor productivity in specific areas of the economy.

The latter are perfectly easy to explain precisely because they occur in

specific times and places and are consistent with the profit-seeking interests

of the entrepreneurs in question, or so the argument goes. Downward

movements in the general price level due to excess demands for money

present Prisoner�s Dilemma problems that changes in factor productivity do

not. The claim is that fractional-reserve free banking can cope much more

satisfactorily with the kind of problem posed by excess demands for money

and accompanying Prisoner�s Dilemma�s than a system subject to a 100 per

cent reserve requirement.

Now Horwitz, and other monetary disequilibrium theorists who hold

similar views, clearly commit a fallacy known as petitio principii. Horwitz�s

argument against 100 per cent reserve banking, namely that such a system

is incapable of coping with a particular kind of problem, presupposes or

assumes what it ought to prove – or at least render plausible - in the first

place, namely that this type of problem could possibly occur under a regime

of 100 per cent reserve banking. Stated differently, the type of problem

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which Horwitz identifies can be expected to occur exclusively under a

monetary regime that is not based on a 100 per cent reserve rule. It is a type

of problem that is indeed particularly likely to occur under a regime of

fractional-reserve banking. But it makes little sense to blame a particular

type of monetary regime, such as a 100 per cent reserve system, for not

being able to cope with a particular type of problem, if under such a regime

such problems would, by virtue of the very nature of that regime, be

prevented from arising in the first place.

In view of such obviously fallacious uses of arguments involving the

Prisoner�s Dilemma model, the question can be raised of whether game

theory may indeed serve as “a gun for hire”. A similar phenomenon has been

observed in other contexts, for instance in political theory. (See e.g. Pellikaan

1994.) Depending upon the situation to which a game-theoretical model

such as the Prisoner�s Dilemma is to be applied or depending upon the

political or ideological agenda of the author who wants to use arguments of a

game-theoretical nature, arguments of this sort may at first appear as

flexibly adaptable. Whereas, say, an advocate of government intervention

may want to choose a one-shot Prisoner�s Dilemma in order to illustrate how

individual rationality “inevitably” leads to a collectively undesirable result, an

author who to the contrary wants to defend free markets will choose a

repeated Prisoner�s Dilemma in order to demonstrate how cooperation can

emerge without central authority (Axelrod 1984 [1990]), thus illustrating the

marvelous achievements of spontaneous orders.

On the other hand, the fact that some uses of game-theoretical

arguments are obviously questionable or fallacious, is no sufficient reason

for rejecting such arguments generally. There can be no general a priori

presumption that Austrians could never make a profitable use of game-

theoretical arguments. (Foss 2000) 5 An illuminating example of a correct

use of Prisoner�s Dilemma reasoning in the context of business cycle

theorizing is provided by Carilli and Dempster (2001). These authors have

used the Prisoner�s Dilemma framework to model the profit maximizing

behavior of bankers and the investors under uncertainty when the market

rate of interest is below the underlying rate of time preference, thus

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questioning the standard account of Austrian business cycle theory which

posits that central bank manipulations of interest rates fool bankers and

investors into believing that there has been an increase in the real supply of

loanable funds available for capital investment.

In the next sections I take a further critical look at several uses of the

Prisoner´s Dilemma model which have been made in the context of the

ongoing debate about free (decentralized) banking, with the purpose of

examining in greater detail the incentives of the banks in a fractional-reserve

free banking system to engage in credit expansion.

2. Does Fractional-Reserve Free Banking Exemplify the `Tragedy

of the Commons´?

Horwitz´ who-goes-first argument invoking the Prisoner´s Dilemma

game is not the only example of game-theoretical Prisoner´s Dilemma

reasoning in the context of the debate on free banking. In the context of the

discussion about the possibilities and limits of credit expansion within a

system of fractional-reserve free banking, the Prisoner´s Dilemma has been

invoked both as supporting an argument in defense of the thesis that

fractional-reserve free banking would exhibit endogenous tendencies toward

concerted credit expansion and as supporting an argument against that

thesis.

In his (2006) Money, Bank Credit, and Economic Cycles Huerta de Soto

uses a Prisoner´s Dilemma model in order to argue that fractional-reserve

free banking will tend to evolve towards the establishment of a system of

central banking, while claiming that what is actually involved is an

application of Hardin´s classic tragedy of the commons theory.6 The effect of

permitting fractional-reserve banking is thus considered analogous to that of

a tragedy of the commons. (De Soto 1998, ch. 8) Therefore, Huerta de Soto

concludes, a return to a banking system subject to a 100 per cent reserve

requirement is to be recommended.

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In the most general sense, the tragedy of the commons refers to the

problem of common property. Inasmuch as property rights are not exclusive,

privately perceived benefits and costs will differ from total gains and costs.

As long as nominal owners and actual holders of rights to rival goods are not

the same persons, the latter are able to use the nominal entitlements of the

former as common property while imposing their use costs on the nominal

rights holders. To the extent of the positive externality, demand for the

resource exceeds the optimal level because others pay its price. The resulting

problem of overexploitation of commonly owned resources may be viewed as

the central problem of property rights economics. Using the terminology of

standard public goods theory, overexploitation is to be expected to occur

whenever the consumption of an asset is rival and non-paying users are not

excluded from extracting benefits from it. (M�ller and Tietzel 1999, 42-3)

Commonplace examples of overuse problems of resources to which no

property rights are assigned are those of natural resources where formal

rights are non-existent, such as air, fishing grounds, oil pools etc. Since

Hardin in his celebrated (1968) article paradigmatically explored his example

of a “pasture open to all”, with many villagers driving on their cattle, the

notion of a “tragedy of the commons” connotes all kinds of examples of

resources with exclusive rights being absent. Each herdsman, as a rational

non-altruist, will try to keep as many cattle on the commons as will meet his

individual profit maximum. While the gains of his effort are strictly private,

the associated costs are shared by all herdsmen, with himself bearing only a

small fraction. Since a similar calculus holds for each individual, the

villagers are locked into a dilemma where collective welfare, which is

maximized at a lower than the individually optimal level of effort, is

unattainable owing to individually rational behaviour.

Two questions can be distinguished in the present context. The first

question is that of whether credit expansion, if it takes place on a more or

less significant scale, indeed generates effects similar or analogous to those

of a tragedy of the commons. The second question, which is more closely

considered here, is whether the internal dynamics of fractional-reserve free

banking is such that effects of this sort would be endogenously generated

16

under this arrangement. Are the effects of fractional-reserve banking indeed

similar or analogous to the effects of the tragedy of the commons in the

sense of Hardin (1968)?

As will be explained further, the interaction configuration between

independent banks in a fractional-reserve free banking system can indeed be

modeled as a Prisoner�s Dilemma. It is less clear - and in fact not quite

correct – that we should also model the tragedy of the commons in the sense

of Hardin (1968) as a Prisoner�s Dilemma. Anyway, it seems intuitively clear

that we would want to conceive of the collectively undesirable outcome, that

is to say the outcome which is inefficient from the perspective of society as a

whole, as corresponding to the inefficient equilibrium in the game, that is to

say the outcome of mutual defection (D-D) in the case of the Prisoner�s

Dilemma.

Huerta de Soto, however, conceives of the interaction pattern between

(initially only two) banks in a fractional-reserve free banking system as a

classic Prisoner’s Dilemma in the manner depicted in figure 1.3. (See also

Huerta de Soto 2006, Table VIII-2 on page 667.)

Figure 1.3

Bank A

Does not Expands

expand

Does not expand R: Survival of both S: Failure of A

Bank B (reduced profits) Survival of B

P: Failure of B Q: Large profits

Expands Survival of A for both

17

In order to bring this representation into better agreement with conventional

textbook representations of the Prisoner�s Dilemma game, we here modify

Huerta de Soto�s representation along the following lines:

(1) The positions of the two players are switched so that Player A becomes

the row player.

(2) It will be noted that in Huerta de Soto�s representation the “inefficient”

equilibrium of this non-cooperative game, which is the outcome in which

both banks abstain from expanding, that is to say the outcome which

represents mutual defection from the standpoint of the banks (D-D outcome

in the Prisoner�s Dilemma game), is located in the upper left corner.

According to the conventional matrix representation of the Prisoner�s

Dilemma game which can be found in most textbooks and which has already

been provided previously, the efficient outcome is located in the upper left

corner while the inefficient Nash equilibrium outcome (solution) is located in

the lower right corner. Although the question of where to locate the

respective – and in particular the main-diagonal - outcomes in the game is a

conventional matter and does not concern the substance of the argument,

for reasons of convenience we again modify the representation along more

familiar lines by putting the mutually cooperative outcome in the upper left

corner.

(3) The ”temptation” payoffs for the unilateral defector (A or B) are labelled

“larger profits for (A or B)” in order to bring out the essence of the Prisoner�s

Dilemma game in which the off-diagonal outcomes act as attractors.

(4) To the C-C outcome which supposedly would yield large profits to both

banks in case this outcome were to occur in one way or another, the

qualifier “in the short run” is added in order to highlight the fact that the

banks apparently adopt a short run, “myopic” perspective in this case, as is

explained further.

(5) Furthermore, following Ludwig von Mises it is assumed that only the

issuance of additional fiduciary media will affect prices and alter the

structure of production. Once the effects of these have been consummated

the market will no longer be influenced by any movements generated from

18

this past credit expansion. As Ludwig von Mises indeed wrote: "The total

quantity of the fiduciary media as issued by the banks and absorbed by the

cash holdings of their clients has altered the structure of prices and the

monetary unit�s purchasing power. But these effects have already been

consummated and at present the market is no longer stirred by any

movements generated from this past credit expansion.” (1998, 434, emphasis

mine)

We adopt the following conventional notation in this respect: ∆CEX > 0

means that Bank X increases its level of credit expansion while ∆CEX = 0

means that Bank X maintains its current level of credit expansion. These

modifications yield the representation depicted in figure 1.4.

Figure 1.4

This conceptualization is intended by Huerta de Soto to

Huerta de Soto intends this conceptualization to elucidate the typical

tragedy of the commons effect which is supposed to appear under fractional-

reserve free banking: bankers face the almost irresistible temptation to be

the first to initiate a policy of expansion, particularly if they expect all other

Interaction Configuration Between Independent Banks

Bank B

∆CEB > 0 ∆CEB = 0

∆CEA > 0 Q: Large profits S: Failure of Afor both Larger profits for

(in the short run) B

Bank A

∆CEA = 0 P: Failure of B R: Survival of both Larger profits (reduced profits)for A

19

banks to follow suit to one degree or another. In a Prisoner’s Dilemma

configuration comprising only two banks, if either bank expands credit

alone, its viability and solvency will be endangered by inter-bank clearing

mechanisms, which will rapidly shift its reserves to the other bank if the first

fails to suspend its credit expansion policy in time. Furthermore, the

situation in which both banks simultaneously initiate credit expansion - a

strategy which yields the same large profits to both - represents the mutually

cooperative outcome, while the situation in which neither of the banks

expands and both maintain a prudent policy of loan concession represents

the outcome of mutual defection.

In fact, there can be little doubt that the interaction configuration

between independent banks in a fractional-reserve free banking system can

indeed be conceptualized as a Prisoner�s Dilemma, in the manner depicted

in our modified representation and as also claimed by Huerta de Soto.

Fractional-reserve free banker White correctly adopts a similar

conceptualization. (White 1995, 16; see further) White is not explicit about

the game-theoretical structure of the interaction pattern he envisages, but

he clearly believes that cooperation between independent banks in view of

concerted expansion would not be a self-enforcing outcome, that is to say

such an outcome is costly to enforce or, stated differently, the interaction

pattern would be of the Prisoner�s Dilemma game type rather than of the

Coordination Game type of interaction. (See also footnote 5.) White�s

reference to the analogy with the breakdown of cartels reinforces this

conclusion since in conventional price theory the breakdown of cartels is

indeed considered perfectly analogous to the Prisoner�s Dilemma. (see e.g.

Landsburg 2002, 399-403) Therefore I will further assume that White has

indeed a Prisoner�s Dilemma type of interaction pattern in mind in this

context.

The interaction pattern between independent banks in a fractional-

reserve free banking system can thus be represented in the aforementioned

manner as a classic Prisoner�s Dilemma. However, the ways in which Huerta

de Soto incorporates this conceptualization into his argument against

fractional-reserve free banking and in favour of the alternative definition of

20

free banking as being based on a 100 per cent reserve requirement, presents

several anomalies:

(1) First, it does not support the aforementioned author�s conclusion that

fractional-reserve free banking will tend to lead to the establishment or the

re-establishment of a central bank. This author indeed argues that it follows

from the aforementioned interaction configuration that the two banks will

face a strong temptation to arrive at an agreement and, in order to avoid the

adverse consequences of acting independently, to initiate a joint

policy of credit expansion, and particularly, to urge authorities to create a

central bank.

Huerta de Soto also writes:

“Therefore our analysis enables us to conclude the following: (…) (2) that the

fractional-reserve banking system itself prompts bankers to initiate their

expansionary policies in a combined, coordinated manner; (…).” (ibid. 670)7

However, and although the aforementioned author�s conclusion may find

some support in historical fact, without a more detailed description of how,

in the absence of extra-market devices and interventions such as those of a

central bank, the two banks will actually coordinate their courses of action

upon the mutually cooperative outcome (in-concert expansion), the

argument is not tight. Indeed, according to the logic of the Prisoner’s

Dilemma game all players will end up defecting so that no overexpansion will

ensue. This is apparently the conclusion L. White (1995, 16) had in mind

when he wrote:

“Concerted expansion by a multiplicity of independent banks is implausible

for the same well-known reasons that the attempt to build a stable cartel

arrangement among many firms is unlikely to be successful in any industry

in the absence of a legal mechanism enforcing cartelisation. Any firm not

abiding by the cartel agreement could capture whatever benefits the

21

agreement is supposed to bring the industry to a greater extent than a firm

adhering to the agreement.”

It may be useful to summarily remind of the role and nature of the

interbank clearing mechanism in this context and its modus operandi in

correcting over-issue by an individual bank. Under a system of fractional-

reserve free banking over-issue by an individual bank will be corrected

through what nineteenth-century writers referred to as a process of “reflux”,

the return of excess currency to the over-issuing bank. Nineteenth-century

writers, when they spoke of the return of excess currency to the over-issuing

bank as a process of “reflux”, emphasized the potential for over-issue. The

contemporary fractional-reserve free bankers believe that an equal amount of

attention should be paid to the potential for under-issue too.

White�s reconstruction of the “law of the reflux” (see e.g. White 1999,

Chapter 3) is based upon the supposition that for any particular bank, there

exists an equilibrium size of its currency circulation – the same is true for its

deposits - that satisfies a set of equimarginal conditions. This size is the

value of the public�s desired holdings of currency issued by bank i, given the

bank�s operating costs, that is to say its optimizing expenditures on non-

price competition.

Let us denote the value of the public�s desired holdings of currency

issued by bank i as N*ip, where the subscript p indicates the public for whom

the currency is an asset, the subscript i denotes the issuing bank for whom

it is a liability, and * means that it is a desired value. It can now be

explained how Nip converges on N*ip as the public adjusts toward its desired

portfolio of assets. Suppose that excess currency is introduced by means of

loans. The borrowers spend the currency. The recipients of the spending now

have balances of bank i currency in excess of their desired levels. A recipient

individual q for whom Niq>N*iq can respond in any of three ways. Direct

redemption for reserves at the issuer�s counter free bankers consider the

least likely way since it is assumed that in a mature system little or no

reserve money is held by the public. Clearly this would directly reduce the

bank�s reserves Ri - as well as in the first place but simultaneously Ni.

22

Deposit of the excess currency into another bank – the bank where q keeps

his demand deposit account - would bring the currency-exchange

mechanism into play, generating adverse clearings for the overissuer as the

recipient bank presents the deposited currency claims for redemption at the

clearinghouse. Settling the clearing balances entails a loss of reserves Ri just

as direct redemption does. The volume of currency in circulation Ni is

reduced by the return of the excess currency to bank i, unless the bank

immediately reissues it. However, the reserve loss signals to bank i that

reissuing the currency would lead to further haemorrhaging of reserves, so it

should accept the reduction in its circulation. Deposit of the excess currency

into bank i itself would not generate adverse clearings. However, it does

mean a higher marginal interest cost of liabilities, and a higher

liquidity cost, than before the expansion. An issuer that was maximizing

profit before will thus find the expansion now unprofitable. Spending the

excess currency transfers the excess to a new individual who also has the

same three options. This new individual will directly redeem or deposit the

currency, leading again to a reserve loss for bank i and a contraction of Ni.

As a consequence of reserve losses, bank i finds its reserves lower than it

desires (Ri<R*i). The marginal net benefit of holding reserves now exceeds the

marginal net revenue from making loans or holding securities, prompting the

bank to sell securities (or not roll over maturing loans) in order to increase

its reserves. Reserves return to bank i from the rest of the banking system.

It would be correct to point out that even if it is true that the inter-

bank clearing mechanism thus limits and puts a check upon isolated

expansionary schemes – expansion by an individual bank – it does not serve

to limit credit expansion in a fractional-reserve free banking system if most

banks "decide" to simultaneously expand their loans, that is to say to

expand in unison. However, assuming a laissez-faire context consisting of a

multiplicity of independent banks, hypothesizing a one-shot Prisoner�s

Dilemma configuration would of course not be a sufficient ground for

arguing plausibly that the in-concert expansion scenario is what will actually

happen.

23

From this perspective Huerta de Soto�s argument apparently assumes

or pre-supposes what it sets out to demonstrate in the first place, namely

the emergence or the existence of a central bank or of a similar device intent

upon orchestrating the in-concert credit expansion by all the banks in the

system. Again the argument seems to involve a petitio principii of sorts.

The breakdown of cartels is indeed perfectly analogous to the

Prisoner�s Dilemma. If a cartel is to succeed, it needs an enforcement

mechanism, that is to say a way to monitor members� actions and a way to

punish those who cheat. (see also Landsburg 2002, 399ff.)

As a model of a tragedy of any sort caused by concerted credit

expansion, the use of the Prisoner�s Dilemma model in the aforementioned

manner is not a convincing representation. According to this very

representation, no tragedy will take place at all. If the two banks play their

unique dominant strategy, the “inefficient” outcome, here characterized by

the absence of credit expansion, will ensue. In this sense the

aforementioned conceptualization is a correct representation of precisely the

opposite of what it claims; it is a correct representation of the absence of any

tragedy.

Therefore the aforementioned one-shot Prisoner�s Dilemma

configuration does not support the conclusion that fractional-reserve free

banking will tend to lead to the establishment of a central bank. Different –

or at least additional - assumptions would be needed to draw this

conclusion. Under laissez-faire, which is the hypothesized institutional

context, mutual defection – characterized by the absence of concerted credit

expansion – is and remains the unique equilibrium.

(2) Second, the outcome which is inefficient from the standpoint of the banks

in the Prisoner�s Dilemma game, is the outcome which is efficient from the

perspective of the rest of society, or from the perspective of society as a

whole, while the cooperative efficient outcome from the standpoint of the

banks – which represents in-concert credit expansion by the entire banking

system - is the outcome which from the standpoint of society must be

considered a tragedy, that is to say sub-optimal.

24

In a conventional game-theoretic representation of a tragedy of the

commons – or of any other tragedy for that matter – we would expect the

efficient, cooperative outcome to be the outcome which represents the

absence of any tragedy, as it may result, for instance, from the imposition of

an adequate property rights regime but which, in the absence of any such

property rights regime, remains the Pareto-efficient but unattainable

optimum. In the absence of an adequate property rights regime, the non-

Pareto-optimal (inefficient) tragedy will ensue in what we would consider an

adequate representation from a more conventional viewpoint.

(3) Third, the Prisoner�s Dilemma modeling does not yet turn the interaction

configuration into a tragedy of the commons in the sense in which this

concept was introduced in Garret Hardin�s popular 1968 paper.

In fact game-theoretically the tragedy of the commons in the sense of

Hardin (1968) is not exactly modeled as a two-person Prisoner�s Dilemma.

The two-person tragedy of the commons is conventionally represented as a

“Stag Hunt” game. In this representation the socially optimal situation

corresponds to the C-C outcome in the game.8 Therefore apparently the

expression ”tragedy of the commons” is used in this context only in a

metaphorical and not in a strictly literal sense, at least insofar as reference

is to be made to Garret Hardin�s 1968 use of this concept.

To the extent concerted credit expansion and its effects indeed present

a genuine analogy with a tragedy of the commons, this analogy results from

three circumstances:

(a) As the Austrian theory of the business cycle explains, credit expansion

engineered by the banks causes large-scale intertemporal discoordination,

misallocation of capital and thus a waste of resources.

(b) According to the advocates of a system of 100 per cent reserve banking,

the deeper causes of this state of affairs can be explained in terms of an

inadequate definition and/or enforcement of property rights.

25

(c) It is assumed that the “tragedy” can be cured by the imposition of a more

adequate property rights regime, in particular a 100 per cent reserve

requirement in banking.

In this sense it is indeed correct to hypothesize that concerted credit

expansion by the banks in a fractional-reserve free banking system, if indeed

it were to occur in one way or another, would constitute a real tragedy of

sorts, somewhat analogous – although not strictly identical - to Hardin�s

well-known tragedy of the commons.

The aforementioned matrix representation, in which the cooperative

outcome yields large profits for both banks, represents a short-run outcome

only. We have noted, however, that under the assumption that the banks

indeed adopt a myopic “self-regarding” perspective by trying to maximize

their short-run profits from credit expansion, the banks are in virtue of the

very logic of the Prisoner�s Dilemma game, and in the absence of additional

assumptions, unable to achieve this outcome since when both banks play

their unique dominant strategy the “inefficient” no-expansion outcome

results.

Moreover, if it is true that credit expansion by the banking system is a

tragedy of sorts, then intuitively we would want to model this fact in such a

manner that the “tragedy” is represented by the inefficient outcome in the

game – in terms of a Prisoner�s Dilemma game: the outcome “mutual

defection” - and the absence of the tragedy by the Pareto-optimal efficient

outcome in the game – in terms of a Prisoner�s Dilemma game: the outcome

“mutual cooperation”. According to the aforementioned representation -

which models the situation from the myopic perspective of the banks and

not from the perspective of society at large - the "efficient" but unattainable

outcome is concerted credit expansion, while the attainable but "inefficient"

Nash equilibrium outcome is the situation in which both banks refrain from

credit expansion. This latter outcome, however, represents the situation

which is efficient from the perspective of society at large. From the

perspective of society at large – but of course not from the short-run myopic

perspective of the banks - one could read the aforementioned model as an

26

argument in favor of fractional-reserve free banking, rather than as an

argument against fractional-reserve free banking.

3. An Alternative Matrix Representation

The assumptions underlying the previous matrix construction are not

compelling, however. Supposing a purely laissez-faire context with no central

bank or lender of last resort, the banks may well acknowledge the fact that

their long-run interests essentially coincide with those of society at large. If

they act imprudently by over-expanding there will be no central bank to

come to their rescue and bail them out.

As is well explained by the Austrian theory of the business cycle, the

huge profits yielded by credit expansion are only a short run phenomenon

and in fact – one could argue – illusory when considered from a perspective

that takes into account the more remote consequences of credit expansion.

The credit expansion engineered by the banking system will set in motion

spontaneous market processes which reverse the distorting effects of the

expansion. Huerta de Soto himself offers an essential clue to better insight

into these matters since he explains in detail in several chapters of his book

how these reversion processes will cause systematic crises in the banking

system. In this sense, while in the short run in-concert credit expansion may

yield huge profits to the banks, the more remote effects of such credit

expansion will, in the absence of a central bank or similar device, be

detrimental to the banks themselves.

If we drop the assumption that the interaction configuration should be

modeled from a myopic “self-regarding” perspective of the banks and if we

reformulate the model from the perspective of society at large by placing the

dominant no-expansion outcome in the upper left corner and by re-labeling

this outcome as one of “Sustainable Economic Growth”, the result depicted

in figure 1.5 ensues.

In this representation the expansive course of action of the individual

banks no longer means “Cooperation” and the prudent course of action of an

27

individual bank no longer means “Defection”. From the standpoint of society

at large, it can indeed be considered efficient that an individual bank which

acts imprudently by unilaterally over-expanding goes bankrupt, and that an

individual bank which acts prudently by restraining from credit expansion

survives and prospers in the long run. Therefore the expansive strategy is

the defective one and the non-expansive strategy is the cooperative one. The

outcomes in which one of the banks defects while the other bank cooperates

are represented by the off-diagonal elements in the matrix. However, these

off-diagonal outcomes no longer function as attractors towards the now

mutually defective (D-D) outcome – as is the case in a Prisoner�s Dilemma

game - since we drop the assumption that the banks myopically pursue the

aim of maximizing short-run profits from credit expansion but instead

assume that the banks recognize the dangers inherent in credit expansion

and thus adopt a perspective that is more in agreement with the long-run

interests of society at large. In this sense one could say it is assumed that

the banks choose “morally” or act in accordance with a “social norm”.

Figure 1.5

Player B (Bank)

Does not Expandsexpand

Does not R: Sustainable P: Failure of Bexpand Economic Survival of A

Player A Growth(Bank)

Expands S: Failure of A Q: TragedySurvival of B

28

Obviously this matrix construction no longer represents a Prisoner�s

Dilemma. Under the previous representation, where it was assumed that the

expansive strategy is the cooperative one and that the banks choose

“egoistically” and “myopically”, Player A�s preference ordering was indeed P >

Q > R > S and Player B�s preference ordering was S > Q > R > P. These were

indeed the orderings which characterize the pay-off structure of the

Prisoner�s Dilemma game.

Under the modified conceptualization where the banks are assumed to

choose “morally” and to act in accordance with the “social norm”, the

mutually defective outcome is the outcome in which both banks choose the

expansive strategy and it is labeled “Tragedy”. The efficient cooperative

outcome is the one in which both banks choose the cooperative strategy by

refraining from credit expansion and it is labeled “Sustainable Economic

Growth”. It is the outcome which is efficient both from the perspective of the

long-run interests of the banks and from the perspective of society at large.

This latter efficient outcome is precisely the outcome that, under suitable

assumptions, will be realized by a free banking system. This representation

illustrates the fact that free banking is an effective mechanism for avoiding

the tragedy resulting from generalized credit expansion. As we have seen,

this conclusion was also implicit in the previous matrix construction. The

modified matrix representation is different, however, in that the no-

expansion outcome is now considered efficient even from the standpoint of

the banks themselves.

Player A�s preference ordering is now, say, R > P > S > Q, while Player

B�s ordering is R > S > P > Q. Clearly this is no longer a Prisoner�s Dilemma

game. This fact illustrates that a modification of the assumptions about the

motives of the players, for instance by assuming that they choose “morally”

or in accordance with the “social norm” rather than “myopically” and in a

purely “self-regarding” manner, radically changes the structure of the game.

In the modified representation it is assumed that the mutually

cooperative outcome in the game represents the situation in which the banks

exercise some restraint by refraining from credit expansion, a course of

29

action which involves foregoing some profit opportunities in the short run

and which in the short run imposes an opportunity cost upon the banks in

the form of foregone short-run profit opportunities. Still it is the outcome

which is in the long run interests both of the banks and of society at large.

Indeed in the longer run the interests of the banks coincide with those of

society at large and it is not too unrealistic to assume that the banks might

conceivably recognize this possible harmony of interests in the longer run.

The outcome in the upper left corner is conceptualized as the

cooperative outcome, not only because it is the efficient outcome from the

long-run perspective of the banks themselves but also and foremost because

it is the outcome which ensures a long-run harmony of interests between the

banking sector and its allies on the one hand and the rest of society on the

other. By refraining from credit expansion the banks act in a manner which

serves both their own longer-run interests and the interests of other market

participants. Of course throughout a laissez-faire context is assumed,

without central banks or similar devices.

In our modified outcome matrix, the outcomes, when considered in

“physical” or objective terms, are identical to the outcomes in Huerta de

Soto�s matrix on page 667 of his (2006) book. Under the modified

representation the outcomes are re-labeled in accordance with their true

significance from the standpoint of society; it is no longer assumed that the

actors in the game will “automatically” perceive the outcome matrix as a

Prisoner�s Dilemma. By abandoning the assumption that the actors – ex

hypothesi the banks in a fractional-reserve free banking system – are

motivated by myopically “self-regarding” considerations, the assumption that

the actors will necessarily attach to the objective outcomes the preference

ordering of a Prisoner�s Dilemma game has been abandoned. Which motives

motivate the actors and which preference ordering they adopt with respect to

the objective outcomes, now becomes a matter for empirical investigation.

The implicit assumption that there exists a one-to-one relationship between

the outcome matrix and the utility matrix, or between a particular outcome

matrix and a particular preference ordering with respect to the outcomes in

that matrix has been dropped. Whenever the banks myopically attempt to

30

maximize their short-run net gains from credit expansion, the preference

orderings adopted by the players (banks) correspond to those of a Prisoner�s

Dilemma: P > Q > R > S for the row player. But whether a bank in a

fractional-reserve free banking system actually adopts a perspective

embracing this preference ordering is an empirical matter. If it is assumed to

the contrary, as we have done, that the banks may adopt a long-run free

market perspective, which leads them to perceive their own interests as

being basically coincident with those of society at large and to choose

“morally” or act in accordance with a “social norm”, the preference ordering

effectuated with respect to the outcomes will no longer be that of a Prisoner�s

Dilemma. For Player A, it may now be, for instance: R > P > S > Q.

Modeling the outcome characterized by the absence of global in-

concert credit expansion as the efficient outcome in the game is also in

better agreement with our intuitions about what is and what is not desirable

for society. It is the outcome which will result if banks take an essentially

long-run perspective, knowing that when they get in trouble there will be no

lender of last resort to come to their rescue. Replacing the laissez-faire

context by a different institutional setting – or lobbying for such a

replacement - is simply not an option for the banks under this hypothesis.

The representation exclusively from the “myopic” short-run perspective

of the banks delivers the intuitively paradoxical result that the mutually

cooperative, Pareto-optimal outcome in the game represents the outcome

which is actually worst from the perspective of society as a whole since, as

the Austrian theory of the business cycle explains, credit expansion by the

entire banking system will distort the productive structure and provoke

widespread, inter-temporal discoordination in the economy. But since the

inevitable reversion effects of the credit expansion process will also hit the

banking sector this outcome is not even efficient from the perspective of the

interests of the banks themselves once a longer time perspective is adopted.

It is indeed far from obvious that, especially from a longer-run perspective,

the outcome consisting of concerted credit expansion by all the banks is in

the interest of the banks themselves since the reversion processes which will

31

necessarily be provoked by the credit expansion will also hit the banking

sector.

The question remains: What is the institutional mechanism to be

imposed to make the efficient outcome the outcome which will actually be

realised? Advocates of the 100 per cent reserve requirement in banking will

contend that obviously this outcome can be achieved by legally imposing a

100 per cent reserve requirement upon the banks, assuming that such a

requirement can be effectively enforced. Advocates of a fractional-reserve free

banking system to the contrary can reply that it seems doubtful from the

perspective of economic theory whether a 100 per cent reserve requirement is

a strictly necessary condition - although it is probably sufficient - for

obtaining the desired result, since even under the pessimistic hypothesis

that the short-term interaction configuration between the banks is to be

modeled as a Prisoner�s Dilemma, the (from the standpoint of society)

efficient no-expansion outcome is the Nash equilibrium solution of the game.

From this perspective imposing a 100 per cent reserve requirement

appears as an instance of regulatory overshooting so to speak, since, as we

have seen, in a fractional-reserve free banking context the inter-bank

clearing mechanism by itself constitutes a sufficient mechanism to

guarantee the desirable outcome. This does not yet mean, of course, that

there may not exist good independent reasons or arguments of an ethical or

of a legal-theoretic nature in favor of the imposition of a 100 per cent reserve

requirement. We are here only concerned with economic logic.

My conclusion concerning the internal dynamics of fractional-reserve

free banking comes thus quite close to that of Ludwig von Mises. Ludwig von

Mises believed that “[o]nly free banking would have rendered the market

economy secure against crises and depressions (…)” (ibid. 440) since under

free banking “a limit is drawn to the issue of fiduciary media.” (ibid. 435) 9

Moreover Ludwig von Mises apparently found no juridical or moral anomaly

in fractional-reserve free banking either. This accords with his general

rejection of considerations grounded in natural law.10

32

Advocates of a 100 per cent reserve requirement in banking might still

question whether the game-theoretical representation indeed captures the

essential characteristics and elements of the interaction pattern between the

banks, thus questioning the conclusion that the interbank clearing

mechanism constitutes a sufficient check upon in-concert credit expansion

by the banks. One such possibility is explored in H�lsmann (2000). This

author conceives of a possible expansive scenario in the following terms. If it

is possible to bring some extra money title into circulation then this

represents an opportunity for other banks to expand their issues. A bank

that receives from one of its customers a money title from another bank can,

rather than present the title to its issuer for redemption, issue more of its

own money titles and “back” them with nothing but the title of the other

bank. This in turn permits other banks - for example, the issuer of the

original “excessive” title - to do the same thing. By this sort of zigzag process,

all the banks can increase their title issues at virtually zero cost. Of course it

is not possible for an individual bank to issue huge quantities of uncovered

money titles at once and all on its own. But over time and in concert with

other banks it can do this through a zigzag process of the sort described.

(H�lsmann 2000, 10) As H�lsmann contends, under fractional reserves, the

cost of currency issue for any given bank is not independent of the decisions

of the other banks. The more titles a bank chooses to hold, the more titles it

can issue, and this permits other banks to do the same thing. In doing this

bankers reduce the title-issue costs of their fellow bankers to virtually zero.

All bankers have a strong incentive to do this since they all gain from the

fractional-reserve business at the expense of the other market participants.

One could add to this account that on Selgin�s and White�s own

account of the working properties of a fractional-reserve free banking

system, this scenario is indeed rather likely to happen since on this account

an increase in the demand to hold on to bank liabilities must lead to an

increase of title issues. This feature of the system is even seen as one of its

main advantages and virtues. Consider the case of an individual bank i

experiencing a rise in demand to hold its currency. (For simplicity the

following analysis is in terms of currency, but the analysis applies equally to

33

deposits.) An increase in the demand to hold bank i�s currency, unmatched

by an increase in the supply, creates the reverse of an overexpansion. As the

fractional-reserve free bankers see it, the actual circulation then falls short of

the desired circulation. Suppose the bank customers, whose demand for i-

currency has risen, hold on to more i-currency instead of spending it. Less i-

currency enters the clearing system, and bank i enjoys positive clearings. As

a result, bank i finds its reserves greater than desired, and is prompted by

the profit motive to expand its loans and securities holdings, increasing its

interest income and ridding itself of undesired reserves. In the new

equilibrium reserves are returned to (or nearly to) their old level, with a

larger volume of i-currency in circulation and a larger portfolio of earning

assets. This is the sense in which according to the fractional-reserve free

bankers the supply of money is demand-elastic: bank i finds it profitable to

respond to a rise in the “desired” level of circulation by raising the actual

circulation, and the reverse for a fall.

However, from the standpoint of the individual banker, it is not prima

facie clear how to distinguish between a situation in which the public holds

on to more of its titles and a situation in which other banks hold on to them,

instead of presenting them for redemption, in view of expanding their own

issue. Thus as soon as, say, bank A holds on to some titles issued by bank B

instead of presenting them for redemption this fact will have for B the same

appearance as an increase in the demand of the public to hold on to its

currency and this fact will thus induce B to issue more titles. Now this fact

allows A to issue more of its own titles with no cost in terms of anticipated

reserve losses. So the point is that each issue of a title not backed by money

represents an additional opportunity for other banks to expand their own

uncovered issues. Each bank discovers how many uncovered titles it can

issue at any point in time; and these issues change the conditions for the

other banks, which can now discover that they can go a little further with

their own issues, and so forth. Since all the banks as well as their clients

have at least a short run incentive to engage into this sort of in-concert

expansion process, it is not obvious anything will restrain this process from

34

running its course. H�lsmann is not explicit about whether this scenario can

be modeled game-theoretically, and if so, how it should thus be modeled.

H�lsmann seems to assume that all banks would obviously be willing to

participate in the expansion. No bank is interested in choosing the strategy

“unilateral defection”. The situation would then probably be better modeled

as a Coordination Game. This is an issue upon which further research on

the topic of free banking along the lines suggested by H�lsmann might focus

closer attention. In any case, and while there is probably no need to deny

that H�lsmann�s scenario is a possible scenario in the short run, it is not

immediately clear why, in a purely laissez-faire context, and in the absence

of a central bank or similar devices, this scenario should be supposed or

assumed to necessarily occur in the real world. The assumption that

“obviously all banks will be willing to participate in the expansion”, thus

manifesting a preference for short-run gains from credit expansion and

neglecting the more remote harmful consequences of credit expansion, is no

more than that: an assumption. It is not logically contradictory to make this

assumption but whether it actually obtains in a historical context is a matter

for empirical investigation in every particular case.

Moreover, as Mises reminds us (1998, 433), free banking is defined by

the fulfillment of two conditions: coexistence and independence of a

multiplicity of banks. If it is simply assumed, however, that no bank would

be interested in taking a course of action which is independent of that of the

other banks, the latter condition is simply assumed away. Again the

argument seems to pre-suppose or to assume what it sets out to

demonstrate in the first place. Therefore, contrary to H�lsmann, we assume

independence of the banks and thus also the possibility of unilateral

defection on the part of any of the individual banks. But then White�s

objection, quoted above, still applies.

In case it is assumed that the interaction configuration is indeed best

modeled as a Prisoner�s Dilemma, a more obvious way to try to counter

White�s objection would seem to consist in modeling the interaction pattern

as a repeated Prisoner�s Dilemma game. Game-theoretical experiments and

arguments have contributed to the understanding of the conditions under

35

which cooperation will be induced by rational self-motivated behavior in

repeated Prisoner´s Dilemma games. (See e.g. Axelrod 1984 [1990].) 11

All of the foregoing is of course not intended to deny that the

introduction of a lender of last resort in the form of a central bank radically

changes the interaction pattern and the incentives of the players. In fact it is

only the introduction of a central bank which leads to the institutionalization

of generalized credit expansion. Independence of the individual banks is no

longer assumed. All the banks participate in the expansion in coordinated

fashion. In any matrix representation the off-diagonal outcomes lose their

significance. The only remaining choices are those between more and less

expansion. The tragedy is unavoidable, but it still makes sense to

distinguish between more or less severe instances of the process. Depending

upon the volume of the expansion and the velocity of the process, the

ultimate effects might appear later or sooner. The dilemma wich arises in

this context is the following: if the monetary authority stops its expansionary

policy, the boom will come to an end and current financial stability may be

endangered; if the monetary authority keeps monetary policy expansionary,

this may help to continue the boom for a somewhat longer period, but only

at the cost of a greater recession later. (see also Bagus 2007)

An approximate matrix construction might then rather yield something like

the pay-off structure depicted in figure 1.6. The whole process is

orchestrated by the central monetary authorities. In this situation in which

the banking system will extract huge amounts of wealth from the rest of

society, clearly the interests of the banking system no longer coincide with

those of society at large.

36

Figure 1.6

4. Conclusion

We can concur with Foss� (2000) conclusion that Austrians ought to

explore ways to incorporate game theoretic reasoning into their analyses,

despite their otherwise highly distinctive and unique approach to the topic of

“microfoundations for macroeconomics”.

An examination of various attempted uses of the well-known

Prisoner�s Dilemma model has also led us to conclude, however, that the

introduction of game-theoretical models into Austrian analyses should

always proceed with great caution. In particular in the context of the ongoing

debate on free banking the Prisoner�s Dilemma model has been used with

varying degrees of perspicacity.

As regards in particular the use of the One-Shot Prisoner�s Dilemma

configuration in the context of an argument against fractional-reserve free

Bank B

More Less expansion expansion

More Tragedy (recession)

Expansion arrives later but is Xmore severe.

Bank A

Less Tragedy (recession)

expansion X arrives sooner

but is less severe.

37

banking, it has appeared that this argument does not support the in-concert

overexpansion thesis and that different – or at least additional - assumptions

would be needed to support this thesis. Nor does it support the thesis that

fractional-reserve free banking will tend to evolve towards central banking.

When modeling the interaction configuration between banks in a fractional-

reserve free banking system, we have abandoned the implicit assumption

that there exists a one-to-one correspondence between the outcome matrix

and the utility matrix. When it is acknowledged that banks in a fractional-

reserve free banking system need not necessarily adopt a “myopic”, self-

regarding perspective but may recognize the long-run harmony of interests

between the banking sector and society at large, a different conceptualization

and a different matrix representation emerge.

38

Notes

1 For a short introduction to capital-based macroeconomics, see Garrison

(2005). For an extensive comparison of capital-based macroeconomics with

other macroeconomic paradigms, see also Garrison (2001).

2 In particular L. M. Lachmann had been especially critical of the style of

thought he characterized as macro-economic formalism. We may speak of

formalism whenever a form of thought devised in a certain context, in order

to deal with a problem existing there and then, is later used in other

contexts without due regard for its natural limitations. (Lachmann 1973, 16)

The schools that adopt the macro-economic approach are tempted to regard

as “macro-variables” what are in reality the cumulative results of millions of

individual actions. Since these micro-economic actions are not necessarily

repeated from day to day, even less from year to year, we have no reason at

all to believe in the aggregative constancy of the macro-variables over time.

(Lachmann 1973, 23) Macroeconomics is safely used only by economists who

are constantly aware of the substructure of individual choices and decisions.

It is unsafe in the hands of economists who think it replaces the

substructure.

3 For a semi-popular account of the history of the Prisoner�s Dilemma, see

Poundstone (1992). Puzzles with the structure of the Prisoner�s Dilemma

were first devised and discussed by Merrill Flood and Melvin Dresher in

1950, as part of the Rand Corporation�s investigations into game theory,

which Rand pursued because of possible applications to global nuclear

strategy. See also: Stanford Encyclopedia of Philosophy, op.cit.

4 These were very well described by Milton Friedman and Anna Schwartz in

their A Monetary History of the United States. ([1963] 1993). As they explain:

“The deposit-currency ratio has been of major importance primarily during

periods of financial difficulties. In each such period, the public’s loss of

confidence in banks led to an attempt to convert deposits into currency

which produced a sharp decline in the ratio of deposits to currency and

strong downward pressure on the stock of money. The establishment of the

39

Federal Reserve System was expected to deprive such shifts in the deposit-

currency ratio of monetary significance by providing a means of increasing

the absolute volume of currency available for the public to hold,

when the public desired to substitute currency for deposits, without

requiring a multiple contraction of deposits. In practice, it did not succeed in

achieving that objective. The most notable shift in the deposit-currency ratio

in the 93 years from 1867 to 1960 occurred from 1930 to 1933, when the

ratio fell to less than half its initial value and in three years erased the

secular rise of three decades. Though the absolute volume of currency held

by the public rose, it did so only at the expense of a very much larger decline

in deposits, the combined effect being a decline of one-third in the total stock

of money.” (Friedman and Schwartz 1993, pp. 684–85)

5 Foss� (2000) main conclusion, namely, that Austrians should approach and

make use of game theory in economics can be granted. This author

emphasized the relevance of the literature on iterated Coordination Games

which is indeed of potential interest to Austrians.

With the proviso provided in the text, we believe that the same is of true of

the literature on Prisoner�s Dilemma games. Whether a Coordination Game

model or Prisoner�s Dilemma game model will have to be used will depend

upon the underlying situation to be modeled. The classic contrast between

Coordination games and Prisoner�s Dilemma games makes perfect sense

since it is illustrative of the fact that whereas surely some forms of

cooperation are easy to reach, others remain prohibitively costly. There is a

sense in which every industry faces a Prisoner�s Dilemma: firms within an

industry could all earn higher profits if they colluded to raise their prices but

individual firms earn more if they continue to compete. It is not difficult to

see why this must be true: consumers prefer low prices to high prices. If all

the other firms collude to charge exorbitantly high prices, the profits of the

deviant firm that undercuts them rise. The difference between a

Coordination Game and a Prisoner�s Dilemma game is reflected in the

difference between standardizing products and fixing prices for instance.

These kinds of business cooperation bear little resemblance to each other

and in fact are radically different. It is confusing to conflate them under the

40

generic heading of “collusion”. As long as consumers want a uniform

product, adhering to industry standards is self-enforcing. As long as

consumers prefer low prices to high prices, price-fixing is not. Reaching the

cooperative outcome in the former may be relatively easy, while reaching this

outcome in the latter case may be costly and difficult. In the case of a price

fixing cartel, the higher prices actually hurt the consumers and this fact is at

the basis of the incentive of individual cartel members to deviate and

continue competing.

6 Hardin�s chief insight was that open access resources will be

unsustainably exploited unless some property rights regime is imposed for

their protection. The question remains which property rights regime. Two

general solutions are typically offered for resolving environmental problems

and both of these are acknowledged by Hardin (1968, 1245): (1) specify

property rights in environmental goods, that is, privatize them, or (2) control

access to and use of environmental goods through governmental regulation.

Therefore most mainstream economists would consider that the existence of

a tragedy of the commons problem per se does not yet constitute an

argument in favour of the first type of solution consisting of privatization, de-

regulation etc. Furthermore it should be noted that law-and-economics

theorists have since long abandoned the idea that private-property rights

have an absolute prerogative to being the efficient institutional form and

have developed the concept of the optimal commons. (e.g. Field 1989; also

Papandreou 1994) Therefore critics might argue that it does not yet follow

directly from any critique of fractional-reserve free banking that a 100 per

cent reserve gold standard would be, in over-all economic efficiency terms, the

obviously preferable alternative. The answer to that question would depend

upon the cost of establishing and sustaining (protecting) the property rights

structure consistent with a 100 per cent commodity standard. The latter

may well remain a costly matter after all, even if on theoretical grounds there

are good reasons to believe that the working properties of such a system

have desirable characteristics in terms of efficiency, stability and

predictability and even on political or ethical grounds, and even if the costs

of a purely fiat standard have tended to be under-estimated until recently.

41

Property rights themselves are costly, and sometimes too costly, to impose

and protect. Therefore the evolution of property rights is seldom

unidirectional, that is to say it does not always move in the direction of more

sharply-defined private rights.

7 It will be noted that this position contradicts that of Ludwig von Mises on

the working characteristics of free banking. See further.

8 A common view is that Garret Hardin�s popular “the tragedy of the

commons” has the structure of a multi-player Prisoner�s Dilemma game.

This contention must be qualified, however. For the matrix representation of

the two-person version of the tragedy of the commons game, see: Stanford

Encyclopedia of Philosophy 2007. On the Stag Hunt, see also Skyrms (2004).

9 Mises explicitly distinguished the problem of the business cycle from the

argument concerning the limitation on the issuance of fiduciary media, and

seems to have related the former predominantly to the hypothesis of in-

concert expansion. He wrote: “The catallactically most important problems of

the issuance of fiduciary media on the part of a single bank, or of banks

acting in concert, the clientele of which comprehends all individuals, are not

those of the limitations drawn to the amount of their issuance. We will deal

with them in Chapter XX, devoted to the relations between the quantity of

money and the rate of interest.”(1998, 433) In chapter XVII on Indirect

Exchange Mises is only concerned with the problem of the coexistence of a

multiplicity of independent banks: “Independence means that every bank in

issuing fiduciary media follows its own course and does not act in concert

with other banks. Coexistence means that every bank has a clientele which

does not include all members of the market system.”(ibid. 433)

10 See e.g. Mises (1998, 716) where he wrote: “There is (…) no such thing as

natural law (…).” Advocates of 100 per cent reserve banking might conclude

that Ludwig von Mises does not seem to have sufficiently appreciated the

importance of the legal-theoretical issues and distinctions involved. Mises

apparently believed that fractional-reserve banking is fully justified from a

“juristic” point of view since he wrote: “It is usual to reckon the acceptance of

a deposit which can be drawn upon at any time by means of notes or checks

as a type of credit transaction and juristically this view is, of course,

42

justified; (…).”(Mises 1981, 300) Significantly he did not link his analysis of

fractional-reserve banking to his important remarks concerning external

effects and the imperfections in the positive or actual definition of property

rights, “loopholes” as he called them. (Mises 1998, 653) As he wrote: “It is

true that where a considerable part of the costs incurred are external costs

from the point of view of the acting individuals or firms, the economic

calculation established by them is manifestly defective and their results

deceptive. But this is not the outcome of alleged deficiencies inherent in the

system of private ownership of the means of production. It is on the contrary

a consequence of loopholes left in the system. It could be removed by a

reform of the laws concerning liability for damages inflicted and by

rescinding the institutional barriers preventing the full operation of private

ownership.”(1998, 653) Clearly an advocate of 100% reserve banking could

argue that the failure to impose and/or to enforce the 100% reserve rule

constitutes a loophole of this sort.

11 See also Kreps et al. (1982) who actually prove that, given a small but

positive probability that one of the players is not really a rational player but

is instead a machine that always plays the tit-for-tat strategy, if there is a

large number of periods then the players will cooperate in every period until

they are close to the terminal period. For a classic and excellent summary of

most of the game-theoretic concepts and arguments, see also Myerson

(1991).

(*) Ludwig van den Hauwe received his Ph.D. from the Universit� Paris-

Dauphine.

43

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